Obtain the expression for a cyclotron and show that it si independan
Answers
Explanation:
Magnetic force on charged particle in magnetic field is give by:
F=qvB
This is equal to the centripetal force acting on the particle.
F=
r
mv
2
=qvB
r
v
=
m
qB
Frequency is given by:
f=
2πr
v
=
2πm
qB
Hence, frequency is independent of velocity of the particle.
(b)
Schematic diagram of cyclotron is attached in the given figure.
It is used to accelerate particles to very high speeds. Protons are injected from a source in a region consisting of orthogonal electric and magnetic fields. The particle feels a centripetal force due to the magnetic field and an accelerating force due to the electric field.
Radius of a particle in the cyclotron is given by:
r=
qB
mv
Hence, given the radius of the particle, speed of the particle can be found. This is used to accelerate the particle to the given value.